Paper-and-pencil nth Roots
As noted above, this algorithm is similar to long division, and it lends itself to the same notation:
1. 4 4 2 2 4 ---------------------- _ 3/ 3.000 000 000 000 000 \/ 1 = 300×(02)×1+30×0×(12)+13 - 2 000 1 744 = 300×(12)×4+30×1×(42)+43 ----- 256 000 241 984 = 300×(142)×4+30×14×(42)+43 ------- 14 016 000 12 458 888 = 300×(1442)×2+30×144×(22)+23 ---------- 1 557 112 000 1 247 791 448 = 300×(14422)×2+30×1442×(22)+23 ------------- 309 320 552 000 249 599 823 424 = 300×(144222)×4+30×14422×(42)+43 --------------- 59 720 728 576Note that after the first iteration or two the leading term dominates the, so we can get an often correct first guess at β by dividing by .
Read more about this topic: Shifting nth Root Algorithm
Famous quotes containing the word roots:
““Jim,” she said earnestly, “if I was put down there in the middle of the night, I could find my way all over that little town; and along the river to the next town, where my grandmother lived. My feet remember all the little paths through the woods, and where the big roots stick out to trip you. I ain’t never forgot my own country.””
—Willa Cather (1873–1947)